'A MANUAL OF 



MECHANICAL DRAWING 



JAMISON 



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Elements of 



Mechanical Drawing 



A COURSE 



IN 



Applied Descriptive Geometry 

arranged for the 

Sophomore Class of Purdue University 

BY 

Alpha pierce Jamison, m. E. 



Assistant Professor of 
Mechanical Drawing in Purdu:^. 



THE LIBRARY OF 


CONGRESS, 


Two Copies 


Received 


JAN 31 


1903 


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XXc. No. 


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COPY 


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Copyright, 1903, 

BY 
A. P. JAMISON. 



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PREFACE. 

The student having' completed a course in Elementary Mechanical Drawing", and 
having acquired a working knowledge of the principles ot Descriptive Geometry as ad- 
ministered in the class room, this work is designed as an advanced course in Mechanical 
Drawing to be administered in connection with the work in Descriptive Geometry as 
typical of problems occurring in practice 

A knowledge, used, is applied knowledge ; the term, "Applied Descriptive Geom- 
etry", is used in the sense, that where in the class room we say, "Find the intersection 
of two cylinders and draw their developments", we here say, "Find the shape and size 
of the two plates forming the elbow", that is, in the class room the subject is treated 
as pure mathematics, here, we speak of practical problems. 

While the intent of these few problems is to show the practical side of the 
Geometry, they are all more or less hypothetical cases, in that all design is omitted, 
the work being preliminary to that subject. 

The remarks on color work are included in this course as many shadow, perspec- 
tive and "show" drawings are often colored. Two colors — black and white— only, are 
used, reducing the cost of an "outfit" to the student, and sufficing for preliminary 
practice. 

The writer is much indebted to Prof. M. J. Golden for many valuable suggestions, 
and to Mr. A. M. Wilson, co-laborer in the administration of the work, for suggestions 
and assistance in the preparation of the plates. 

LaFayette, Indiana, January, 1903. A. P. J. 




CONTENTS. 



PART J. 



EXERCISES. 



INTERSECTIONS AND DEVELOPMENTS, ETC. 
Section. Page. 

1 General Instructions ' 3 

2 Problem 1. — To lay out the cutting lines for g^etting out the wreath starting- 

from a newel poit , .— 5 

3 Problem 2. — To lay out the man-hole plate for a boiler 7 

4 Problem 3. — To locate, and find the leng-th of guy wires for a smoke stack 9 

5 A sheet of free-hand letters 11 

6 Problem 4. — To find the shape, size and bevels of an example in cabinet 

work _ 13 

7 Problem 5. — To find the shape and size of the plates used to form an elbow 15 

8 Problem 6, 7 and 8.— To lay out certain sheets on a locomotive boiler 17 

9 Problem 9, — To find the length and necessary bevels for a diagonal brace 23 

10 Problem 10 — To execute an isometric drawing 25 

11 Problem 11. — To lay out the plates for a screw grain conveyor 27 

12 Problem 12. — To find the shape and size of certain plates forming part of a 

positive feed mechanism 29 

13 Problem 13. — Given the four elevations of a house, —to draw the roof plan 35 

14 Problem 14. — To execute an isometric drawing 37 

SHADO WS. 

15 Problem 15. — To find some elementary shadows 41 

16 Problem 16. — To find the shadows cast by a plane figure 41 

17 Problem 17. —To find a shadow on a single curved surface 41 

18 Problem 18. — To find a shadow on a double curved surface 41 

19 Problem 19. — To find the shadow cast by a 1'' set collar 42 

PERSPECTIVE. 

20 Problem 20. — To find the perspective of a cube, a prism, and a cylinder 47 

21 Problem 21. — To find the perspective of a fligiit of steps... 47 

22 Problem 22. — To find the perspective of a house 48 

23 Problem 23.^ — An original problem in perspective .—, 49 

COLOR WORK. 
Tinting. 

24 An elementary exercise 53 

25 Some representative surfaces 55 

26 A practical example 57 

Stippling. 

27 Some representative surfaces _ ; 59 

28 A practical example _ _ 61 



PART 2. 
REFERENCES. 

SHADO WS. 

29 Introductory — - — — . 65 

30 Theory of shadows... ..._. 65 

31 The shadow of a point _ 65 

32 The shadow of lines 65 

Straig'ht and curved. 

The shadow^ falling on one plane only. 

The shadow falling- on both planes. 

The shadow of a line which is parallel to one of the planes of projection. 

33 Outline for finding' shadows 67 

Example — The shadow of a rectangular solid. 

34 The shadow on the object - 67 

PERSPECTIVE. 

35 Definition of perspective drawing _ 69 

36 Perspective and mechanical drawing compared 69 

37 Mechanical and free-hand perspective 69 

38 Perspective as applied by the engineer ..- 69 

39 Theory of perspective..... _ 69 

40 The perspective of a point 71 

41 The perspective of a right line 71 

42 The perspective of a curved line 71 

43 Perspective reduced to conventional orthographic projection 71 

44 Objects assumed in the second quadrant ,-— - 71 

45 The perspective of an indefinite right line 71 

46 The vanishing point of a line 72 

47 Rule for finding- the perspective of a line — 72 

48 Two special cases of the line 72 

49. Conventional method for finding perspectives 73 

50. The plan revolved into the iirst quadrant _ — 73 

51. The horizon line 73 

52. The application of the distance points _ 73 

53. Practical perspective 74 

COLOR WORK. 
Tinting. 

54 Introductory 76 

55 Outfit .._ 76 

56 Making a stretch...... „ 76 

57 Mixing the color , 77 

58 Flat wash _ 77 

59 Sh ading .._ _ 77 

Different methods. 
Stifling. 

60 Introductory 79 

61 Method of procedure 79 



PART L 
EXERCISES 



EXERCISES IN FINDING 

TRUE LENGTHS, TRUE ANGLES, 

DEVELOPMENTS, ETC 



GENERAL INSTRUCTIONS, 



GENERAL INSTRUCTIONS FOR DRA WING. The paper used for the 

course is the standard sheet of the department for small work, i.e., 8 "x 11" border, 
finished sheet, 9' ' x 12' '. Each exercise has all necessary dimensions g-iven either 
on the plate or in the instructions; some ot the exercises are full sized drawings, 
others, to some proportional scale. For some exercises, dimensions for balancing- the 
drawing on the sheet are given; in every case these figures represent full size 
lengths and are to be omitted on the finished drawing. 

The exercises are to be taken up in the order set forth and each sheet 
numbered"] in^ the upper right hand corner; the first to read, " Sheet No, 1," the 
second, " Sheet No. 2," and so on throughout the course. 




Plate No. 1. 



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EXERCISES. 



PROBLEM 1 TO LAY OUT THE CUTTING LINES FOR -^GETTING OUT" 
THE WREATH STARTING FROM A NEWEL POST Let the problem 

be that presented by Plate I and let it be required to show the " lay out " in " iso- 
metric." As may be seen by the plate, the wreath is the curved portion of the 
band-rail. Such a piece is usually cut from a block; to find the size of the block, 
enclose the mechanical drawing's - plan and elevation - of the wreath within rec- 
•tang-les; the length of the block will equal the lenglh of either rectangie - the 
leng"ths are the same -the width will equal the width of the rectangle enclosing" 
the plan drawing-, and the thickness of the block will equal the width of the rec- 
tangle enclosing the elevation drawing. In laying out the cutting lines on the 
block, the top face will contain the plan of the wreath, and the right side, the 
elevation drawing; these lines laid out, the wreath is sawed out by cutting along 
them. The drawing shows a rectangular rail; in practice the rail is of a section 
calculated to be ornamental, and useful as a grip for the hand; such a section is 
carved in the wreath after cutting out as above. 

The isometric drawing is constructed according to the principles of isometric 
drawing- as set fo-artli in the Descriptive text, by first drawing the above enclosing- 
planes - the outline of the block- then locating the wreath within. 
DIRECTIONS FOR DRA WING. Execute a scale drawing according to 

the dimensions, drawing the plan first, then the elevation, then lay out the block. 
Draw all necessary lines in light pencil, then submit the drawing for inspection. 
In inking, ink only those lines shown on the plate, g'ive all dimensions - supplying 
those marked X - and finish the sheet by lettering as shown. 

NOTES 



Plate No. 2. 




EXERCISES • 7 

PROBLEM 2. TO LA Y OUT THE MAN-HOLE PLATE FOR A BOILER. 
Let -the problem be that presented by Plate 2 showing two sections through an 
elliptical man-hole. Assume we have a sheet of boiler plate which we wish to 
first roll to the contour of the outside of the boiler - 60" outside diameter - then to 
" flang-e in " as shown, to form a seat for the man-hole plate. The practical prob- 
lem would envolve an allowance for the "flow of metal " and for planing off the seat, 
however the student may disregard both of these, and let it be required to find the 
dimensions A and C of the elliptical opening which is cut in the plate before 
" rolling up." 

The principles of geometry envolved in the solution of this problem are, 
'• With the two axes given, to construct an ellipse; an example of simple projection 
in constructing the longitudinal section, and a simple development in finding the 
dimensions A and C." 

Begin with the transverse section, then draw the two full-line ellipses, then by 
projection, draw the longitudinal section?; next straighten - turn up - the flange, 
obtaining dimensions A and B, then draAV this ellipse; this done, develope the plate - 
flatten it out - obtaining dimensions C and D, then draw these ellipses. 
DIRECTIONS FOR DRA WING. Execute a scale drawing according to the 

dimensions, drawing all necessary lines in light pencil, then submit the drawing 
for inspection. In inking, ink only those lines shown on the plate, give all dimen- 
sions — supplying A, B, C and D — and finish the sheet by lettering- as shown. 

NOTES 



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EXERCISES 9 

PROBLEM 3. TO LOCATE AND TO FIND THE LENGTH OF GUY WIRES 
FOR A SMOKE STACK. The principles of g-eometry envolved in the 

solution of this problem are, "To find the point in which a g^iven line pierces a 
given plane, and to find the true length of a line." 

Let the problem be that presented by Plate 3. A power house of the shape - 
roof half pitch ( 45" ) - and size given, is to have a forty-two inch stack, guyed by 
six guys arranged as shown, and making an angle of 45° with the stack; the con- 
ditions are such that two of the guys vvrill strike the roof plane, and let it be re- 
quired to locate the ground end of each guy and to find its length. 

A cable suspended as in this example, would not assume a straight line as 
shown, but would assume a curve, however for the problem we will take the hypo- 
thetical case of the straight line. 

To find the points in which the guys pierce the ground, revolve one of 
them parallel to the vertical plane and note the distance of the point in which the 
vertical projection of the guy strikes the ground line, from the point in which the 
vertical center line of the stack intersects the ground line; with this length as a 
radius, and the horizontal projection of the center line of the stack - the center of 
the circle-as a center, describe a circle intersecting the horizontal projections of the 
guys; these points of intersection will be the horizontal projection of the points in 
which the guys pierce the ground and may be located by referring to the foundation 
of the building. The true length of the guys reaching the ground, is evidently the 
length of the 45° line on the vertical plane,- the vertical projection of a guy when 
parallel to V. 

To find the point in which the guy on the right pierces the roof plane - the ex- 
ample on the left is a case of simple projection, the plane of the roof here, being 
perpendicular to V — we note that the plane of the roof strikes the ground B dis- 
tance from the foundation, which enables us to draw the trace of the roof plane 
(t-T-t',') and with the projections of the guy given, we have but to find the point in 
which these projections pierce the plane T. The true length of the guys are found 
by revolving them into parallelism with V. 

DIRECTIONS FOR DRA WING Execute a scale drawing according to the 

dimensions, drawing all necessary lines in light pencil, then submit the drawing for 
inspection. In inking, omit all construction lines, give all dimensions -> supplying 
the required lengths - and finish the sheet by lettering- as shown. ' f 

NOTES 




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EXERCISES ■ 11 

A SHEET OF FREE HAND LETTERS. Execute the sheet, by first 

drawing- top and bottom g-uide lines in light pencil, then ink - free-hand - directly, 
without any preliminar}^ penciling- of the letters. The student is to make choice 
of size of letter and spacing- for the sheet by comparison with the copy. 

NOTES 





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EXERCISES 13 

PROBLEM 4. TO FIND THE SHAPE, SIZE AND BEVELS OF THE 
THREE PIECES FORMING THE TRIANGULAR OBJECT SHOWN IN 
PLATE 5, AND TO FIND THE ANGLES BETWEEN THE PIECES. The 
problem is typical of problems occuring- in carpentry and cabinet making- and 
envolves the principles of geometry, "To find the true length of a line and to find 
the true size of an angle " 

Sufficient dimensions are given that the section of each piece may be found, 
then each piece is revolved about one of its edg-es, into parallelism with the hori- 
zontal plane; a position which shows all edg-es in their true length and position 
relative to one another, and from which the bevels may be found. 
DIRECTIONS FOR DRA WING. Execute a full sized drawing according to 

the dimensions, drawing the plan drawing first, then the elevation, then draw 
the sections; taking one piece at a time, assume it to be removed to one side, then 
revolve it into parallelism with H; scale this drawing and supply the dimensions 
marked X. To find the angles D, E, F, G, H and I, pass a horizontal projecting 
plane perpendicular to one side of the bevel, this will cut the required angle, which 
may be shown by revolving the plane parallel to H. The angles between the pieces 
are found by adding the bevels of each piece as shown by the plate. 

In addition to the above statement, let it be required to draw a half size iso- 
metric drawing of the object, taking dimensions from the mechanical drawing. 
This is done in accordance with the principles of isometric drawing" as guven in the 
Descriptive text. 

DIRECTIONS FOR DRA WING. Draw all necessary lines in light pencil 

then submit the drawing for inspection. In inking, ink only those lines which 
appear on the plate, give all dimensions and finish the sheet by lettering as shown. 

NOTES 



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EXERCISES 15 

7 PROBLEM 5. TO FIND THE SHAPE AND SIZE OF THE PLATES USED 
TO FORM AN ELBO W. I<et the problem be that presented by Plate 

6 and let it be required to lay out the templates for the three plates forming- the 
elbow, the allowances for lap and joints being dis-reg-arded 

The principles of g-eometry envolved in the solution of this problem are, " To 
develope a right cylinder of circular section, and to develope an oblique cone." 

Analysing- the elbow, we note that it is composed of three figures; "A" and "C,"' 
which are right cylinders of circvilar section, and " B," which, by extending the 
limiting elements, is seen to be an oblique cone. 

To develope the plates, first pass a number of common intersecting planes in- 
tersecting the three figures in elements- for convenience, it is suggested these 
planes be made to divide the bases into an equal number of equal arcs, twelve being 
a good working number -then beginning with cylinder "A," lay off the line X-Y-X 
equal to the circumference of "A" and erect the perpendiculars representing- the 
elements cut by the intersecting planes; the vertical lengths of the elements are 
taken directly from the elevation drawing of "A" and through the extremes, 
the curve 1-1, representiag the line of the upper base of the c/linder, is drawn 

To develope the cone " B," the true length of each element must be obtained 
by revolving it into parallelism with the horizontal plane ( this is a third angle pro- 
jection ) and with the length of the lower base of the cone known — for since the 
cone " B " is fitted to cylinder " A," the circumference of the bases are equal — we 
proceed to construct development " B " as follows : — Select a center point C and 
draw the center line C-G-7 equal in length to the true length of element 7-7. ( It 
should be noted that the figures are cut along the outside element, -elevation draw- 
ing — cut by the intersecting plane 1-C of the plan drawing-). With C as a 
center and a radius equal to the true length of element 6, describe an arc; then 
with point 7 as a center and a radius k, taken from the development of cylinder 
" A," describe an arc intersecting the first arc, the point of intersection, c, will 
be the locus of the lower base end of element 6; this element may then be drawn 
by connecting points e and C; similarly combining the true length of each element 
with the proper distance between elements, taken from development "A," we 
obtain a series of points l-a-b-c-etc, through which the line 1-7-1, representing 
the developed circumference of the lower base of the cone, is drawn. With these 
points and the center point C known, it is a simple proceedure to lay off the true 
length of each element and throug-h the extremes, to dr^w the developed line of the 
upper base and thus complete the development of fig-ure " B." 

In figure "C," we have a right cylinder neither base of which is at right 
angles to the elements. To develope this cylinder we can assume an intermediate 
base m-n, the plane of which is perpendicular to the elements and which will 
develope as the straight line m-n; this line is used as a base line for drawing the 
development, the method of proceedure being- similar to that used for developing 
cylinder "A." 

A drawing of these three, developments executed on heavy paper, cut out and 
duplicated in wood or sheet metal, or the paper used directly and laid on a sheet of 
metal for '■ laying out," would be called a " template " for the job. 
DIRECTIONS FOR DRA WING. Execute a scale drawing according to 

the dimensions, drawing" all necessary lines in light pencil, then submit the drawing 
for inspection. In inking, omit all construction lines, give all dimensions and 
finish the sheet by lettering as shown. 



Plate No. 7. 




EXERCISES 17 

PROBLEMS 6,7 and 8. TO LAY OUT CERTAIN SHEETS ON A LOCOMOTIVE 
BOILER. Plate 7 showing- a skeleton drawing- of a type of locomotive, 

illustrates a number of typical problems in intersections and developments met 
with in sheet metal work. Six plates - those numbered - are choosen for examples 
and mechanical drawing- of each, given at the bottom of the plate. 

Following the instructions on the plate, let the development of the three 
plates forming the stack constitute Problem 6; the development of plates 4 and 5, 
Problem 7, and of plates 6 and 7, Problem 8. 

Analysing- each sheet, we note the stack to be composed of a right cylinder, 
circular in section (No. 3), and two rig'ht cone shaped sheets (No.'s 1 and 2 ); 
No.'s 4 and 5 are examples of the intersection of two right cylinders, circular in 
section, at right angles, -the stack and the dome being the respective "intersecting- 
cylinders ; " No. 6 is half right cone and half right cylinder, each circular in sec- 
tion, and No. 7 is an example of the intersection of two right cylinders at rigfht 
ang-les, one :)f which is elliptical in section and the other circular in section. 

The geometrical surfaces being- now known, apply the principles of geometry 
for the development of these surfaces to the problems in hand, arranging- Problem 
6 as shown on Plate 8, Problem 7 as on Plate 9. and Problem 8 as on Plate 10 ; these 
plates depict all working lines as suggestive to the student. 

DIRECTIONS FOR DRA WING. Execute a scale drawing of each 

plate in accordance with the copy, drawing all necessary lines in light pencil, 
then submit the drawing for inspection. In inking-, omit all construction lines, 
give all dimensions— supplying those marked X — and finish the sheet by lettering 
as shown. 

NOTES 



Plate No. 8. 




Plate No. 9. 




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EXERCISES 23 

PROBLEM 9. TO FIND THE LENGTH AND NECESSARY BEVELS FOR 
A DIAGONAL BRACE AND TO CONSTRUCT A WORKING DRA WING FOR 
" GETTING OUT" THE BRACE. Let the problem be that presented 

by Plate II illustratin<f a frame constructed of four by four timbers, for which we 
wish a diagonal brace, with its center line passing through the apex of the angles 
as shown in the front elevation drawing, and 2" in - half way - from the outside 
as shown in the plan drawing. 

The principle of geometry envolved in the solution of this problem is, "To 
find the true leng-fh of a line," a simple problem in the Descriptive Geometry though 
here it is some what complicated because of the relation of each line of the brace 
to other lines; in the Geometry it is a simple revolution of a single line, here as the 
line is revolved, its relation to the other lines must be maintained. 

The brace being oblique to both planes of projection necessitates two revolu- 
tions, first into parallelism with the vertical plane, ( this is a third quadrant pro- 
jection ) then from this position into one of parallelism with the horizontal plane, - 
a position parallel to both V and H and showing the edges of the brace in their 
true length. 

DIRECTIONS FOR DRA WING. Execute a scale drawing according to the 

dimensions, drawing the front elevation first, then the plan, then draw the side 
elevation; revolve the plan drawing of the brace about the point C as a center, until 
the center line m'-n' is parallel to V, then find the corresponding elevation draw- 
ing; this drawn, revolve the brace about point C as a center, to a position par- 
allel with H and find the corresponding plan drawing; these two drawings will 
represent the plan and elevation of the brace showing all the edges in their true 
length; these true length views are re-drawn to a scale of 3' ' = 1' as shown, and an 
end view added; this drawing is to be the working drawing, the dimensions marked 
D, to be supplied. 

Draw all necessary lines in light pencil, then submit the drawing for inspection. 
In inking, ink only those lines shown on the plate, give all dimensions and finish 
the sheet by lettering as shown. The sheet is not to be passed in until the isomet- 
ric drawing of the brace — the next sheet — has been completed. 

NOTES 



t# 



Plate No. 12. 




EXERCISES 25 

10 PROBLEM 10. TO EXECUTE AN ISOMETRIC DRA WING OF PROBLEM "i. 
An isometric drawing is much used for representing" simple rectangular objects such 
as the frame and brace in question, also such a draught stich as the proposed one 
prepared from the mechanical drawing, is of value to elucidate the job to the work- 
man who cannot understand the mechanical drawing. 

DIRECTIONS FOR DRA WING. Find all dimensions by scaling the 

mechanical drawing, then in accordance with the principles of isometric drawing 
as set forth in the Descriptive text, execute a full sized drawing according to 
Plate 12. Draw all necessary lines in light pencil, then submit the drawing for 
inspection. In inking, ink only those lines shown on the plate and finish the sheet 
by lettering as shown. 

NOTES 




Plate No. 13. 




EXERCISES 27 

11 PROBLEM 11 TO LAY OUT THE PLATES FOR A SCREW GRAIN 

CONVE YER Let the problem be that presented by Plate 13 wh^ch illus- 

trates ( small model ; a portion of a form of g-rain conveyer, and let it be required 
to lay out the blade in the most economical manner for punching from sheet metal. 

The problem is typical of a form of convever of a wide range of usefulness; 
post hole augers, the helical, inclined plane up which the circus performer a-foot 
of a ball or astride a wheel wends his way, are other examples of the surface. 
For punching, it is evident that by laying out the blade in two sections for each 
convolution we can eifect a saving of material, and disregarding the question of 
lap and method of fastening to the ceatral core —items to be considered in actual 
manufacture — let it be required to develope the blade. 

Inspecting the figure we recognize a practical application of the right helicoid, 
and the principle of geometry envolved in the solution of the problem is, "The 
development of a right helicoid." This being- a surface of double curvature — a 
warped surface— theoretically we cannot develope it, though practically we can' 
very closely approximate it. 

To develope the tig-ure, draw the straight line 1 - 1 equal to the true leng'th of 
an element— it is evident all the elements are of the same leng-fh — then find the 
true distance between elements, inner and outer ends, — these lengths are also uni- 
form; this distance is the true length of the cord of arc Band of arc A, respectively. 
With these lengths as radii and the extremes of line 1—1 as centers, describe arcs 
as shown Next find the true leng-th of the diagonal C, which gives the last of the 
lengths required for the development; Cl being this length, and dimension E 
the length of an element, the various lengths are combined as shown and the points 
1, 2, 3, etc , obtained; these points form the locus of the developed curves forming 
the extremes of the elements. 

A carefully executed drawing will be found to closely approximate a circle, and 
by using any three points of either extreme, the center of the circle may be found 
and the arcs drawn. ' 

DIRECTIONS FOR DRA WING. Execute a full sized drawing according 

to the dimensions, arranging the punchings as shown; draw all necessary lines in 
light pencil, then submit the drawing for inspection. In inking, omit all construc- 
tion lines, give all dimensions — supplying dimensions marked D — and finish the 
sheet by lettering as shown. 

NOTES 



Plate No. 14. 




EXERCISES 29 

12 PROBLEM 12. TO FIND THE SHAPE AND SIZE OF CERTAIN PLATES 
FORMING PART OF A POSITIVE FEED MECHANISM. In Problem 11 

we find a practical application of the right helicoid; the oblique lielicoid is also of- 
ten met with in practice. It is obvious that the sides of a square thread are right 
helicoids; the sides of a V thread are examples of the oblique helicoid. 

Suppose we wish to construct a V threaded screw of plates of metal, to 
form a positive feed for some such mechanism as the house wife's food grinder. 
This is named as an example because of its familarity, though in this apparatus 
the "sere " is usually of cast iron. The more usual application of the oblique 
helicoid is in certain forms of screw propellers for boats, vanes for water wheels, 
in positive pressure blowers, etc. 

Assuming that if one side of the screw thread can be laid out the other side 
may be readily obtained, the problem deals with a single face of the thread and is 
presented by Plate 14 illustrating- ( small model ) one convolution of this face,, 
the problem being to develope the plate shown. 

The figure is a warped surface, hence the development can only be approxi- 
mated. The method of proceedure is exactly as given for developing the right 
helicoid of Problem 11; dimensions Al, Bl. Cl, and E ( see development) being 
equal to the true distance between elements— inner and outer extremes — the true 
length of a diagonal and the true length of an element, respectively; it is 
evident that these dimensions are uniform throughout tlie development, and when 
laid out, will be found to so closely approximate a circular arc that a center may be 
found and the curves drawn as arcs of circles. 

DIRECTIONS FOR DRA WING Execute a full sized drawing according 

to the dimensions, drawing all necessary lines in light pencil, then submit the 
drawing for inspection. In inking, ink only those lines shown on the plate, give all 
dimensions, supplying dinensions marked D — these would be necessary for laying 
out on a sheet of metal— and finish the sheet by lettering- a shown. 

NOTES 



Plate No. 15. 




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Pirate No. 16. 




Plate No. 17. 





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Plate No. 18. 




Plate No. 19. 




EXERCISES 35 

13 PROBLEM 13. GIVEN THE FOUR ELEVATIONS OF A DWELLING 
HOUSE. TO DRA W THE ROOF PLAN AND TO FIND THE TRUE LENGTH 
OF ALL HIPS, RIDGES AND VALLE YS. The first part of the 

problem — to draw the roof plan — is a test of the student's understanding" ot the 
relation of the four elevations; the latter part of the problem is a practical example 
of the application of that principle of geometry enabling one to find the true 
length of a Hue. 

To draw the roof plan, no dimensions being given, the elevations are to be 
measured with the scale or dividers, and the various lengths transferred to the 
drawing. In laying out the hips, ridges and valleys in practice, certain allow- 
ances are made for finish, in this case all such allowances are disregarded. It is 
obvious since all ridg"es are parallel to the ground, these lengths may be scaled 
directly as drawn; the hips and valleys — lines inclined to the horizontal — may be 
projected on a parallel profile plane and the projections measured. i 

DIRECTIONS FOR DRA WING. Execute a full sized drawing of the 

first floor plan —Plate 15— by scaling the copy, then on this drawing draw in the 
roof plan as suggested above, drawing all n2cessary lines in light pencil, then 
submit the drawing for inspection. In inking-, omit all construction lines, dash all 
hidden lines — those forming the first floor plan which the roof would hide — andfinish 
the sheet by giving the required lengths by writing them alongside the lines. In 
scaling the drawing for these lengths, assume the drawing to be to a scale of 
1-16" = 1'. 

This drawing is not to be handed in at this time, but it is to be retained as is 
will be required for drawing- the next sheet, and later in drawing a perspective of 
the house. 

NOTES 



Plate Xo. 20. 




EXERCISES 37 

14 PROBLEM 14. THE FOUR ELEVATIONS AND ROOF PLAN GIVEN, TO 
CONSTRUCT AN ISOMETRIC DRA WING OF A D WELLING HOUSE. Let 

it be required to depict the right and rear elevations. No dimensions being" given, 
the drawings are to be scaled. 

DIRECTIONS FOR DRA WING. Assume the house to be enclosed within 

a rectang'ular plane figure; draw this enclosing figure in isometric, then proceed — 
working from the mechanical drawings — according to the principles of isometric 
drawing as set forth in the Descriptive text, using Plate 20 as a guide. 

Execute a full sized drawing, drawing all necessary lines in light pencil, then 
submit the drawing for inspection. In inking, omit all construction lines and finish 
the sheet by lettering as shown. 

NOTES 



NOTES 




EXERCISES 

IN FINDING 

CAST SHADOWS. 



Note — 

Before proceeding-, read the Reference on Cast Shadows. 



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EXERCISES. 41 

15 PROBLEM 15. TO FIND SOME ELEMENTAR Y SHADO WS. Let 
the problem be that presented by Plate 30 ( lower half), — to find all the shadows 
cast by the objects shown. The principle of g-eometry envolved in this and all 
other examples of shadow finding is, "To find the point in which a right line 
pierces the planes of prejection." 

DIRECTIONS FOR DRA WI.\G. Execute a full sized drawing- of the 

fig-ures according- to the dimensions, assuming- the ground line 3^'' above the lower 
border line. Draw all necessary lines in light pencil, then submit the drawing- for 
inspection. In inking, rule the shadow with very lig^ht lines, omit all dimensions 
and construction lines, and finish the sheet by lettering as shown. 

16 PROBLEM 16. TO FIND ALL THE SHADOWS CAST BY A FIGURE ALL 
THE FACES OF WHICH ARE PLANE SURFACES. Let the problem be 
that presented by No. 1, Plate 21. An inspection of the figure shows it to be made 
up of lines, each of which is parallel to either V or H, — a fact which should be 
taken advantag'e of in the solution of the problem. 

DIRECTIONS FOR DRA WING. Execute a full sized drawing- according- 

to the dimensions, assuming the g-round line and arrangement of the figure so as 
to produce a well balanced sheet. Draw all necessary lines in lig-ht pencil, then 
submit the drawing' for inspection. In inking, omit all dimensions and construct- 
ion lines, rule the shadow and finish the sheet by lettering- as showii. 

17 PROBLEM 17. TO FIND ALL THE SHADOWS CAST BY A FIGURE THE 
FACES OF WHICH INCLUDE PLANE AND SINGLE CURVED SURFACES 
Let the problem be that presented by No. 2, Plate 21. An inspection of the figure 
shows the single curved surface to be a cylinder, and the bottom edges of the plane 
surfaces to be parallel to H. 

The new feature introduced by the problem is the finding of the shadow on the 
cylindrical surface; an example is made of the point P, through the horizontal 
projection of which we pass the horizontal projection of a ray, r ; this is seen to 
strike the cylinder at a, — the shadow of point P on the cylindrical surface — appear- 
ing as a' on the vertical plane; by taking a number of points as P, and finding 
their shadows in the same manner, we obtain a number of points defining- the locus 
of the curved line limit to the V shadow on the cylinder. 

DIRECTIONS FOR DRA WING. Execute a full sized drawing according- 

to the dimensions, assuming an arrang-ement which will produce a well balanced 
sheet. Draw all necessary lines in light pencil, then submit the drawing for in- 
spection. In inking, omit all dimensions and construction lines, rule the shadow, 
and finish the sheet by lettering- as shown. 

18 PROBLEM 18. TO FIND ALL THE SHADOWS CAST BY A FIGURE THE 
LACES OF WHICH INCLUDE PLANE. SINGLE AND DOUBLE CURVED 
SURFACES. Let the problem be that presented by No. 3, Plate 21. The 
figure here depicted is typical of the niche— recess — in a wall in which a statue is 
placed, the upper part being spherical or dome shaped, and the lower part cylin- 
drical. 

To find the shadow cast on the figure; a point P is choosen for an example of 
the shadow on the single curved surface, this shadow is seen to fall at A, — as in 
Problem 17. The new feature here introduced is the finding of the shadow on the 
double curved surface, a second point P being- taken for example. Through this point, 
aray Rispassedand throug-h the ray, its horizontal projecting plane; this plane will 
cut the curve l'-2'-3'-4' from the surface To find this curve, a number of vertical pro- 
jecting planes parallel to H (s', s', s', s') are first passed through the figure inter- 



42 EXERCISES 

secting- it in the semi-circles s, s, s, s; then project the points of intersection of 
plane T with the traces of these planes onto the surface, and since all lines in a 
plane pierce the plane of projection in the trace of that plane, ray R pierces the 
surface at X. In this manner a number-of points are obtained — the last of which 
is the tang-ent point Y — through which the curve defiuingthe outline of the shadow 
is drawn. 

DIRECTIONS FOR DRA \Vh\ G. Execute a full sized drawing- according 

to the dimensions, assuming" an arrangement for balancing" the sheet. Draw all 
necessary lines in lig'ht pencil, then submit the drawing- for inspection. In inking, 
omit all dimension and construction lines, rule the shadow, and finish the sheet by 
lettering as shown. 
19 PROBLEM 19. TO FIND ALL THE SHADOWS CAST BY A ONE INCH 
SET COLLAR WHEN IN TWO DIFFERENT POSITIONS. Let the 

arrang-ement be that depicted by Plate 22— the ground line is in center of the sheet 
DIRECTIONS FOR DRA WING. Execute a full sized drawing according 

to the dimensions, draAving all necessary lines in light pencil, then submit the 
drawing for inspection. In inking, omit all dimension and construction lines, rule 
the shadow and finish the sheet by lettering as shown. The isometric drawing is 
to be omitted. 

NOTES 



Plate No. 22- 





NOTES 



EXERCISES 

IN 

FINDING PERSPECTIVES, 



Note — 

Before proceedino-, read the Reference on Perspective. 



Plate No. 23. 




EXERCISES 47 

20 PROBLEM 20. TO FISTD THE PERSPECTIVE OF A CUBE, A PRISM AND 
. A CYLINDER. Let the problem be that presented by Plate 23— lower 

left hand corner — the lig-ht line drawing^s being the mechanical drawing-s — plan 
and elevation— of the objects, from which the heavy line drawinj^s representing" the 
perspectives are to be found. Let the perspective be found by the "perpendicular 
and diag"onal" method. 

DIRECTIONS FOR DRA WING. Execute a full sized drawing- according to the 

Plate, the cube being 2' ' on an edg-^ and the hole. 2' ' square; the prism, 2' ' between 
flats and the cylinder, 2' in diameter; B-L is the border line of the sheet. Draw 
all necessary construction lines in light pencil, then submit the drawing- for inspec- 
tion. In inking-, omit the original mechanical drawing's and all dimension and con- 
struction lines, show the perspectives only, and finish the sheet by lettering- as 
shown. 

21 PRORLEM 21. TO FIND THE PERSPECTIVE OF A FLIGHT OF STEPS. 
Let the mechanical drawing- for the steps be the plan and elevation drawing-s of 
Plate 23; let the gTound line be >^ ' ' above the lower border line ( B-L ) and let the 
picture plane be at 30 with tfie front faces of the steps Here we have all lines 
either parallel or at 30^ or 60" with V; find vanishing- points for these lines, then 
proceed as in Sect. 53. 

DIRECTIONS FOR DRA WING. First pencil a full sized plan and 

elevation drawing- of the steps according- to the dimensions, then cut the paper 
seperating- the views, and arrang-e them on the drawing" board as illustrated by the 
Plate. Draw all necessary lines in lig-ht pencil, thea submit the drawing- for 
inspection. In inking-, omit all constrviction lines, and finish the sheet by lettering" 
as shown. The plan and elevation drawing's are not to be handed in. 

NOTES 



Plate No. 24. 




EXERCISES. , 49 

22 PROBLEM 22. TO FIND THE PERSPECTIVE OF A SMALL DWELLING 
HOUSE. Let Plates 15, 16, 17, 18, 19 and Sheet No. 14— the drawing- of 
the roof plan — be the mechanical drawing-s of the house, and let it be required to 
picture the front and left sides. Let the student assume the point of sight and gen- 
eral arrangement. Plate 24 shows a perspective which is 30° with the picture plane 
and the horizon line at the height of a man's eye when standing- on the ground, 
which according to the scale of the drawing, is on a level with the door knobs. 
DIRECTIONS FOR DRA WING. Use sheet No 14 for the plan drawing, 
the elevations maybe cut from the book if so desired, or the heights of the various 
points laid off on the drawing paper as needed, by scaling the plates. Select an 
arrang-ement, then submit the drawing for inspection, Draw all necessary lines in 
light pencil ( it is not necessary to draw any lines whatever on the plan drawing; 
the various points may be projected to the ground line with the triang-le, and 
checked thereon ) then submit the drawing" for inspection. In inking, omit all 
construction lines and finish the sheet by lettering as shown. 

23 PROBLEM 23. EXECUTE AN ORIGINAL PROBLEM IN PERSPECTIVE. 
Before proceeding submit the proposed problem for approval. 

NOTES 



NOTES 



EXERCISES 

IN 

COLOR WORK. 



Note — 



Before proceeding-, read the Reference on Color work. 



■i 



Plate No. 25 




53 



TINTING. 



24 AN ELEMENTARY EXERCISE. PLATE 25. This is a first exercise 

for the brush. Stretch the paper and use black ink, — prepared by rubbing- the 
stick of ink in a saucer containing- a small quantity of -water. 

DIRECTIONS FOR DRA WING. Lay out the sheet according to the dimensions, 
in light pencil, being careful to draw only the lines necessary to block out the rec- 
tangles—do not draw lines -within these spaces necessitating an erasure, thus 
bruising the surface, as this -would sho-ft- through the wash. Begin with 1 and wash 
in the top row of rectangles; it will be noticed that the shade increases in depth as 
we proceed to the right; this is accomplished by, after each wash, rubbing the stick 
of ink in the saucer, — the tint should be inspected by sample on scrap paper before 
applying. 

The shaded row is washed in in accordance with the third method of shading 
given in the reference. It should be noted that 7-A and 7-B are alike and are the 
light washes of the row ; that 8- A and 8-B are alike and are a shade deeper than 
7-A and 7-B, and that 9-A and 9 B are alike and are the heavy shade of the row. 

The tinted row is washed in by first laying a fiat wash over the entire rec- 
tangle, and when dry, applying the shade as above. 

In the flat wash, (top row,) let the paper be first washed with clear water for one 
or two spaces, that the student may note the effect ; the remainder of the sheet may 
be washed in directly. 

In executing the sheet, exercise great care in preserving the outline of the rec- 
tangles; should the color run outside, the edg-es may be straightened with a knife 
point and eraser, a procecdure, however, which does not add to the beauty of the 
sheet and is to be avoided if possible. 

In inking, ink only the border line of the sheet — not the borders of the rec- 
tangles — omit all dimensions, and finish the sheet by lettering the title and name 
only. When finished, cut the paper from the board with a. }4' ' margin outside of the 
border line on all sides. 

NOTES 



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Plate No. 26. 




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EXERCISES 55 

25 SOME REPRESENTATIVE SURFACES. PLATE 2b. This sheet is a 

wash drawing of plane surfaces parallel with and inclined to the plane of projec 
tion, and of concave and convex single curved surfaces. 

To wash figure 1, begin on the left with the proper tint and draw it out to the 
right, washing entirely across the rectangle — do not attempt to define the center 
edge ; when dry, begin at the center with the proper tint and draw out to the right. 
For 2, flat wash the parallel face and when dry, shade the inclined sides as shown. 
B^or 3, lay on a light wash first, then treat each face in order according to the degree 
of shade. For 4, beginning at the left, draw out the tint to the right and entirely 
across the rectangle : when dry, begin at the right side and draw the tint to the 
left. For 5, flat wash the flat surfaces first, then shade as in 4. 

The next row, representing end views of the figures in the top row, are all flat 
washes. For 6, flat wash the circular drawing, also the rectangular section, first 
cross hatching it with the ruling pen and the wash ink. The shading of this 
figure may be done according to the fourth method of the reference Figure 7 is a 
flat wash of three tints. For figure 8, the circular drawing is a flat wash of two 
tints, and the rectangular drawing, a wash similar to the rectangular drawing of 6. 
DIRECTIONS FOR DRA WING. Lay out the sheet according to the 

dimensions, in light pencil ; wash all flat surfaces first, then shade as directed above. 
In inking, ink the border only, and finish the sheet by lettering the title and name. 



Plate No. 27. 




EXERCISES. 57 

26 A PRACTICAL EXAMPLE. PLATE 21. This sheet illustrates certain 

well known mechanical details, washed in as for catalogue illustration, and intro- 
. duces the application of chineese white for bringing- out the lines. Figure 1 repre- 
sents a coil spring ; 2, a section of a cylinder, disclosing a piston ; 3. a portion of a 
square threaded bolt and 4, a hexagon headed bolt and nut, — 5 and 6 are end views. 

To shade the spring, cross hatch the sections wiih the ruling pen, using wash 
ink, then flat wash them ; shade the front of the spring- first, then the parts show- 
ing at the rear. To shade, use the fourth method of the reference and wash in 
one curvature at a time : i. e. , consider the top wire extending across the front of 
the spring ; beginning- at the top. la}' on a stripe of the tint all the way across, then 
draw it down at once; when dry, begin at the bottom line and draw up at once ; when 
dry, begin at the left hand, lay on the wash and draw to the right at once ; when dry, 
shade the right end in a similar manner. 

The cylinder is shaded in a like manner, — one curvature at a time The sec- 
tion is cross hatched, free hand, with the tip of the brush, then flat svashed. 

The thread is also shaded one feature at a time. 

To shade the bolt and nut, wash in all the flat surfaces, then shade as above. 

The white lines are ruled in with the ruling pen and chineese white ink ; this 
is done the last thing before handing the sheet in. 

DIRECTIONS FOR D^A WING. Lay out the figu.'es according to the 

dimensions, wash in as directed and finish the sheet by lettering as shown. 
All dimensisns are to be omitted. 



J 



Plate No. 28. 




59 



STIPPLING, 



27 SOME REPRESENTATIVE SURFACES. PLATE 2%. We have depicted 

here the plan and elevation of a hexagonal prism, a hexagonal pyramid, a cone 
and a cylinder. The figures are first drav^^n in outline on a duplicate sheet, that is, 
the figures are laid out in the same arrangement relative to one another and to the 
border line as they are to occupy on the stippled sheet. 

Now with a knife point cwX out the plan of the prism, cone and cylinder ( 5, 7, 
and 8 ). The first and last are flat surfaces and are stippled uniformly by placing 
the "stencil " on the sheet, border to border, and the dots thrown through the 
openings as directed in the reference. To shade the plan of the cone ( 7 ), mat out 
with strips of paper, all of the exposed surface except a small sector in the part to 
be darkest ; stipple about as for the flat surfaces, drawing the shade at the radii ; 
now increase the a ea of the sector, then stipple lightly again this will cause the 
first shaded portion to gTow darker. Continue increasing the size of the sector in 
this manner until the entire circle is exposed when the view will have been shaded. 

For the plan of the pyramid (6 ), cut through the stencil on the lines repre- 
senting the elements, and part way through on the base lines ; with the stencil in 
position, fold back the lower right hand triangle and stipple rather dark ; now fold 
back the bottom triangle — the first remains open— and shade the exposed area; 
next fold back the upper right hand triangle and shade the exposed surface ; pro- 
ceed in this manner, taking the faces in the order of the degree of shade and shade 
the entire exposed area each time, thus causing the faces to grow darker in the 
order of exposure. 

To shade the top row, 1, 2, 3 and 4, cut out the side faces of the prism and of 
the pyramid, and the outlines of the cone and cylinder ; place the stencil in position 
and shade the exposed surfaces according to the copy, care being taken to protect 
each surface after stippling; these shaded, cut out the front face of 1 and 2, and 
stipple the exposed areas. 

DIRECTIONS FOR DRA WING. In stippling, it is important that the 

stencil be protected, that is, when stippling an area, mat out the surface of the 
stencil immediately about the opening, with scrap paper, thus keeping the moisture 
off the stencil, which if allowed on, would cause it to blister; also, it is important 
that the stencil have good contact with the paper to produce clean cut lines, — good 
results are obtained by laying small weights about the edges of the opening. 

In inking, ink the border line only, omit all dimensions and finish the sheet by 
lettering as shown. 



Plate No. 29. 



SiiMKfi'.f :;■ - 'S'&*saff «.•--:.-■ ■»*. 




EXERCISES. 61 

28 A PRACTICAL EXAMPLE. PLATE V). Here we have depicted for 

" show" purposes, a form of insulator ( 1, 2 and 3) and an ornamental cap (.4, 5, 
and 6 ). The figures are first drawn on the stencil paper, then the sheet executed 
in the following- order: — 

Cut out 1, the interior of 2, the darkest- circle of 3, all of 4, the interior of 5 and 
the center of 6 ; place the stencil on the sheet, border to border, weight the 1' ' center 
of 1 and 3 in position, and shade the exposed areas according- to the copy. Next 
cut out the section of 2 and 5, the second circle of three and all of 6, then shade. 
Now cut out the ends of 2, all of 3 and the double curved part of 5 ; mat out with 
scrap paper the exposed parts already stippled, then shade ; lastly, cut out the 
g-roove of 3, and the single curved surface of 5 ; mat out exposed parts and shade 
according to the copy. 

DIRECTIONS FOR DRA WING. Ink the border line only, omit all 

dimensions and finish the sheet by lettering- as shown. 

NOTES 



^ 



PART 2. 
REFERENCES 



^ 



65 



SHADOWS. 

29 INTRODUCTOR V. Without light and shade a drawing is merely a flat 
out-line. A simple out-line drawing, shade or back lined, answers for usual shop 
purposes ; for catalogue and show purposes, it is sometimes desirable to have a 
drawing depicting the light and shade. The preparation of such drawings is a 
trade in itself, however, the engineer, at times, may desire to produce a handsome, 
shaded drawing, and having a knowledge of shading to convey form (cylindrical, 
inclined, concave and convex surfaces, etc.) — he may enhance his work by the 
addition of shadows. 

It is the purpose of these notes to impart a working knowledge of the finding 
of cast shadows — a practice seldom resorted to in ordinary, commercial mecnanical 
drawing, though used to some extent in architectural work. 

30 THEOR Y OF SHADO WS. The rays of light are assumed as eminating 
from the sun, and coming from such a distance, are assumed parallel and usually 
at 45° to the planes of projection. Now assume a point in space, this will, of 
course, intersept one of the many rays of light ; this ray, un-obstrtfcted, would reach 
and pierce one of the planes of projection, but being intersepted by the point, the 
ray does not reach the plane of projection and we have a point thereon v^^hich is 
not illuminated — a point in shadow ; hence to find the shadow of a point in space, 
pas-5 a ray of light (it must be remembered, a point is assumed by its two projec- 
tions, also, a ray of light is assumed by its two projections), through the point 
and find the point in which this ray pierces the planes of projection. 

It is obvious that a point will cast its shadow on but one of the planes of pro- 
jection, — a shadow point on the ground line being an exception. For all usual 
shadow work, objects are assumed situated in the first quadrant, and the shadow 
is cast on that plane first pierced by the ray of light. In all the following discus- 
sions, consider the first quadrant only. 

31 THE SHADO W OF A POINT. In Fig. 1, Plate 30, let p, p' be the hori- 
zontal and vertical projections, respectively, of the point P in space, — to find the 
shadow cast by P. Through the point pass a ray of light (p-P and p'-P') and 
find the point in which this ray first pierces the planes of projections. This 
point is seen to be point P' on the vertical plane of projection, hence P' is the 
required point, — the shadow of P. Fig. 2 illustrates the shadow of a 
point P, so situated that it ( the shadow ) falls on plane H. 

32 THE SHADO W OF LINES. To find the shadow of a right line, « e have 
but to find the shadow of any two points in the line and join the shadow 
points by a right line. If the line be of a given length, the two extremes are the 
points choosen. If the line be a curved line, the shadow of several of its points 
is found and the^-e shadow points, joined by a curved line. 

THE SHADO W FALLING ON ONE PLANE ONL Y. Fig. 3 illus- 

trates the shadow of a line so situated thit it ( the shadow ) falls entirely on the 
vertical plane. 



Plate No. 30. 




REFERENCE-SHADOWS. 67 

THE SHADO IV FALLING ON BO TH V AND H. In Pig. 4, let 

m-n and m'-n' be the projections of a line M-N, and let it be required to find its 
shadow. Through the extremes, M and N, pass rays of light and find the point 
in which these rays pierce both V and H: then join the two V shadows by a right 
line, also by the two H shadows by a right line, these will intersect in the ground 
line, and since we are to consider but the first quadrant, the heavy line M-X-N' is 
the required shadow. 

THE SHADO W OF A LINE WHICH IS PARALLEL TO ONE OF THE 
PLANES OF PROJECTION. Fig. 5 illustrates a line M-N (m-n 

and m'-n') which is parallel to H, and M-N its shadow on H, which we note to be 
parallel and equal to M-N ( m-n ), hence, the shadow of a line on a 
parallel plane, is parallel and equal to the line itself, — it being a case of parallels, 
comprehended between parallels. This is an important point to be fixed well in 
mind, as this understood, greatly expedites the finding of shadows. 

33 OUTLINE FOR FINDING SHADO WS. The process of finding cast 
shadows is the repeated application of, "Find the point in which a right line 
pierces the planes of projection," a first problem in the Descriptive Geometry and 
a very simple procedure, provided one Icnows which and how many lines to use. 
The first step then, in finding the shadow of a certain object, is to have a full nnd 
correct knowledge of the form of the object, then construct a mechanical draw- 
ing of it— assuming the object by its projections — portraying these features. 
The second step in the work, is to study the mechanical drawing, assuming 
each view to be the object, that is, assume the object to project from the paper, to 
have form, and with the direction of the rays of light known, think out just what 
points and lines will cast shadows — a procedure which properly followed, will, 
after some practice, g-reatly reduce un-necessary work and thus faciliate the 
drawing. 

EXAMPLE, -THE SHADOW OF A RECTANGULAR SOLID. Let 

Fig. 6 represent the projections of a rectangular solid, a-b-c-d (lower base) — 
A-B-C-D ( upper base ) being the horizontal projection, and the primed letters, 
the vertical projection, and let the direction of the rays of light be as indicated, — 
to find the shadow cast by the solid 

Considering the object as above and reasoning that rays through 
points nearest the horizontal plane will strike the planes first, and that rays 
through points most remote from H will strike the planes later, we observe that 
a-d-c of the lower base casts the first shadow; that the line of contact of the rays 
with the figure, then runs up the edges a-A and c-C, and that the edges A'-B'- 
C of the upper base casts the latter shadow; we then have the limits df the 
shadow, its outline, for, wliile the other edges may cast shadows, these fall 
within the outline and are not considered as it is the outline of the shadow 
that is required. 

34 THE SHADOW ON THE OBJECT. Fig. 7 illustrates an object 
of such form as to cast shadows on itself. Consider the rectangular projection 
at the top; passing a ray through point A, we note that it strikes the fig'ure 
at 4', which point is horizontally projected as 4, and since the line A-X is par- 
allel to the plane on which the shadow falls, we draw the line 4-Y paralled to 
A-X. (Section 33 ) The full shadow of A-X on the plane, would, also, be equal to 
A-X, — a length which carries the outline of the shadow beyond the edge of the 



68 REFERENCE-SHADOWS. 

fig^ure, when it is then projected onto H, and falling within the outline of the 
shadow on the plane, receives no further consideration. Passing a plane of rays 
through point B, completes the shadow of the rectangular feature. Now consider 
the recessed portion of the object; it is evident that the edge C-P will cast 
a shadow on this portion. To find this shadow, pass a ray of lig'ht throug^h point 
C, this pierces the figure at point 5, and since the line C-P is parallel to the 
plane on which the shadow falls, the shadow is completed by drawing- through 
point 5, parallel to C-P . The shadow of the figure on the planes V and H is 
found as in Sect. 30. 

Fig". 8 illustrates the shadow cast by an ordinary spool; to find the 
shadow of the circular planes, it is necessary to divide the circumference into a 
number of points and throug-h these, pass rays of light piercing" V and H — as the 
ray R through point P, piercing V at S, — thus locating a number of points de- 
fining" the locus of the outline of the shadow. 

To find the shadow on the figure itself, consider the horizontal projection, 
where we note that a plane of rays through X is a tangent plane, and that all 
that portion of the figure beyond X, (to the right ) is in the shadow, hence, the 
vertical projection of the shadow is obtained by drawing the vertical line X'-X' ; 
in like manner, the tangent plane at Y, produces the perpendicular Y'-Y', and we 
have the shadow on the figure as shown. 

NOTES 




69 



PERSPECTIVE. 

35 DEFINITION OF PERSPECTIVE DRA WING. Perspective Drawing, 
or Linear Perspective, commonly called "Perspective", is the art of representing 
an object or objects, on paper or other plane surface, in such a manner as to pre- 
sent the object as it would appear when viewed from a definite view point. 

36 PERSPECTIVE AND MECHANICAL DRAWING COMPARED. Per- 
spective diflFers from mechanical drawing, which presents an object in detail — 
each face or side separately and as it really is and not as it appears to the eye — in 
that it presents the object as a whole — showing several faces or sides in a single 
drawing — and as it would appear if viewed from a gnven standpoint. 

37 MECHANICAL AND FREE HAND PERSPECTIVE. These terms 
are used relatively, the mechanical perspective being drawn, mechanically, from 
and after mechanical drawings have been constructed, while the free-hand perspec- 
tive covers the work of the artist, thoug^h in this connection (mechanical drawing) 
is meant the free-hand perspective sketch prepared from mechanical drawings or 
from the object. 

38 PERSPECTIVE AS APPLIED BY THE ENGINEER. The art of 
perspective drawing is of minor importance to the eng-ineer, his conceptions be- 
ing best expressed by simple mechanical drawings, an exception being, to the 
afchitectual engineer perspective drawing is of equal importance with mechanical 
■drawing, in that in his work it becomes necessary to show how the finished work 
will appear. 

Perspective is of value, however, to any engineer, as often in the shop a 
perspective sketch prepared from a mechanical drawing, will eluciate the draught 
to one to whom it was unintelligable, also, the art is of value when it is desired to 
picture some proposed work, as a factory, a dam, etc., hence it becomes import- 
ant that all engineers should have a working- knowledge of the principles of per- 
spective drawing. 

The examples and remarks following are not designed to produce expert 
perspective draughtsmen, but as the fundamentals — with the exception of finding 
shadows in perspective— are given, when these are understood, with practice one 
may become quite expert in the art. 

39 THEORY OF PERSPECTIVE. If from a finite point of sight we view 
an object, the lines of sight will converge at the eye, — we see with two eyes but in 
perspective a single point of sight is assumed and to make the analogy correct, 
assume the observer to close one eye; now if these lines of sigiit be intersected by 
a plane — usually assumed to be between the object and the point of sight, for 
reasons explained later — and the points in which the several lines of sight pierce 
it be properly connected, we will have a drawing representing the object, de- 
creased in size, exactly as it appears to the observer. 

The intersecting plane assumed in practice, is the vertical plane of ortho- 
graphic projection — being assumed because of its position, which enables us to 
place objects to be pictured, with a large number of their principle lines either par- 



Plate No. 31. 



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o 




o 










^ 






^ 






^ 






l°... 




O / 


^ 




\v 




/ 




^' 


~Q. 




/ 


/ 




/ 




^ 


^.. 


■Q 





Si- 




k 


(S 







Q: 





o 



PERSPECTIVE. 71 

allel or perpendicular to the plane, thus expediting- the work of constructing^ the 
perspective — and is called t':ie "plane of the picture", while the orthographic pro- 
jection of the point of sight on this plane is called, the "principle point of the 
picture". 

40 THE PERSPECTIl'E OF A POINT. Let Fig-. 1, Plate 31, illustrate 
the planes of projec.on, V being- the vertical plane— the plane of the picture — and 
let S represent the point of sight in space and situated in the first quadrant, also, 
let M represent :i point in space, situated in the second quadrant — thus placing 
the picture plar.e. V, between the point and the point of sight -and let S-Mi -M, 
represent the line of sight. To find the perspective of point M, we have but to 
find the point in which S-Mi -M pierces plane V. (Sect. 39.) By orthog-raphic pro- 
jection, we fin 1 this point to be Mj , — the perspective of point M. 

41 THE PERSPKCTIVE OF A RIGHT LINE. In Fig 1, let M-N represent 
a line in space, second quadrant, let S be the point of sight, first quadrant, 
and let S-Mand S-N represent lines of sight, — to find the perspective of M N. 

Since the line is a right line, we have but to find the perspective of two 
points in the line and join them by a right line. If the line be of a given length, 
as in this case, the two extremes, M andN, are the points used. By orthographic 
projection, these points are found to be Mx and Ni , and the perspective to be 
Ml -Ni . 

42 THE PERSPECTIVE OF A CURVED LINE. The perspective of 
a curved line is found by linding the perspective of a number of its points, and 
joining them by a curved line. 

43 PERSPECTIVE REDUCED TO CONVENTIONAL ORTHOGRAPHIC PRO- 
JECTION. In Fig. 5, ^Ye have the above example reduced to 
conventional orthographic projection. Consider first, the finding of the per- 
spective of point M. Since in all orthographic projection a point is as- 
sumed by its two projections, the point M is assumed by its two projections, m 
and m',-m being the horizontal and m' the vertical projection, and the point of 
sight, S, by the projections s and s'; also, the line of sight S-Mi -M is shown by 
its two projections s-m and s'-m'. By the usual method, we find the line S-M i- 
M ( s-m and s'-m' ) pierces V at Mi — the perspective of M. 

Considering the point N in the same manner, we find point Ni to be its 
perspective, which, joined by a right line with Mi , gives the perspective Mi -Ni 
of the line M-N. 

44 OBJECTS ASSUMED IN THE SECOND QUADRANT Fig. 
6 represents a profile view of the arrangement depicted in Fig. 5, and shows 
the converging lines of sight, from which it is obvious that as plane V — the pic- 
ture plane — is moved towards M-N — the '-object'" m this case — the perspective be- 
comes larger, and when moved towards S, the picture becomes smaller, also, it is 
evident that when the picture plane is beyond M-N, the picture will be larger than 
the object. As in nearly every case, a picture smaller than the object is de- 
sired, objects are assumed situated in the second quadrant and the point of sight 
in the first quadrant. 

45 THE PERSPECTIVE OF AN INDEFINITE RIGHT LINE. Since 
to find the perspective of any right line, we have but to find the perspective of 
any two points in the line and join them by a right line, we may proceed as in Sect. 
41, and through the two points thus found, draw an indefinite right line, or, 
since the line may be assumed of infinite length, if not parallel to the picture plane. 



72 PERSPECTIVE. 

it will pierce the plane in a point, which point is clearly a point in the perspective 
of the line, and we then have to find, by the usual method, the perspective of but 
one additional point, and throug-h these two points, draw the indefinite perspec- 
tive. If the line be parallel to V, we deal with any two points. 

46 THE VANISHING POINT OF A LINE. If we have two parallel 
lines, they are said to meet at infinity. Assume two such lines, one, a line in space, 
and two, a line parallel to it, throug'h the point of sig'ht; these two lines being- no 
exception to the rule, will meet at infinity. Now assume the parallel line throug'h 
the point of sight, to be the line of sight to the meeting point at infinity; the point 
in which the line pierces V will be the perspective of that point. Since the lines 
meet in a point, they are said to vanish there, and this point is called the "vanish- 
ing point" of the lines, from which we deduce, the vanishing point of a line 
is where a line parallel to it, through the point of sight, pierces the picture plane. 

EXAMPLE. In Fig-. 2, let m-n and m'-n' be the horizontal and 

vertical projection, respectively, of the line M-N, and let s and s' be the like pro- 
jections of the point of right S,-to find the vanishing point of the line M-N. 

Through point s, the horizontal projection of the point of sight, draw the 
line s-v parallel to line m-n — the horizontal projection of M-N — and through point 
s', draw s' — v' parallel to m'-n' — the vertical projection M-N; these two lines — 
s-v and s'-v' — represent the projections of a line S-V throug-h the point of sig-ht, 
parallel to M-N. By the usual method, S-V is found to pierce V at v', which 
point is the vanishing- point of M-N. 

The figure shows the perspective { Mi -Ni ) of the line M-N, as found by 
Sect. 41, also, the perspective Mi -Ni extended, when it is seen to pass through 
point v' — the vanishing- point of the line. 

From the above, it is evident that a system of parallel lines has a com.mon 
vanishing point, for the line through the point of sig-ht, parallel to one line, is par- 
allel to all; hence the common vanishing point. 

47 RULE FOR FINDING THE PERSPECTIVE OF A LINE. Since all 
lines may be extended and considered to be of indefinite length, by combining 
Sect's. 45 and 46, we have the following definitive rule: — 

The perspective of a line is a line joining the point in which it {the line) pierces 
the picture plane atid its vanishing point. 

48 TWO SPECIAL CASES OF THE LINE. 1. THE DIAGONAL. In per- 
spective, a line which is parallel to H and at 45° with V, is called a "diagonal"; in 
Fig. 3, let m-n and m'-n' be the projections of a diagonal M-N; s and s', the 
projections of the point of sight S, and let it be required to find the vanishing 
point of the diagonal. By Sect. 46, we find this point to be d' (left-hand.) 

Now assume m-n — the horizontal projection of M-N — to be revolved into 
the first quadrant as m' '-n' ', and note that s-d (left hand) is parallel to the 
original position of m-n and to the real line, M-N, and that d' (left hand) is the 
vanishing point for m' '-n' '. For reasons stated later, it is convenient to assume 
the horizontal projection as having been revolved into the first quadrant, and when 
working with such conditions, a diagonal inclined to the right, as 
m'-n'', vanishes to the left of s', that is, to that side of the vertical 
projection of the point of sight, op'posite to the direction of the inclinaton of the 
line. 

It should be noted that the point d', either right or left, is distant from 
s', as far as S^is from the picture plane, — the line s-d being 45°. 



PERSPECTIVE. 73 

Note also, that diag-onal X-Y, vanishes at d' (right hand), same distance 
from s' as d', (left hand). 

In practical perspective, the vanishing" points for diagonals are called 
"distance points," and are assumed and no mention made of s — the horizontal 
projection of the point of siglit. 

2. THE PERPENDICULAR. -In perspective, a line which is 

perpendicular to the picture plane is called a "perpendicular"; it is evident, all 
such lines vanish at the point of sig'ht. 

49 CONVENTIONAL METHOD FOR FINDING PERSPECTIVES. If we 
have a point in space and pas's two lines through it, then find the perspectives of 
the two lines, the intersection of the perspectives will be the perspective of the 
point For reasons which will later become apparent, this seemingly round- 
about method, is the usual proceedure in practical perspective. The two lines as- 
sumed for this purpose are a diagonal and a perpendicular. 

EXAMPLE. In Fig. 4, let p, p' be the projections of a point P, 

s, s', of the point of siglit, and let it be required to find the perspective of P. 

The diagonal through the point pierces the picture plane at D', and van- 
ishes at d', hence, D'-d' is its perspective; the perpendicular through the point 
pierces V at p', and- vanishes at s', hence, p'-s' is its perspective; the intersection 
of these two perspectives. Pi , is the required perspective. 

In the figure, the elementary method (Sect. 40) of finding the perspec- 
tive of the point is also given, that the student may note the "check" of the two 
methods. 

50 THE PLANT RE VOL VED INTO THE FIRST QUADRANT Fig. 7 
illustrates the elementary method of finding the perspective of a cube, s and s' be- 
ing the point of sight, H-H-H-H, the horizontal projection of the cube and V-V- 
V-V its vertical projection, — the perspective is indicated by the heavy line draw- 
ing. We note that the plan and elevation — H and V projections— of the cube, 
over lap in the drawing, producing confusion; assume the plan to be 
revolved into the first quadrant, as indicated by the dashed position, and apply 
Sect. 49, as in Fig 8, — a procedure which avoids the confusion and is that 
adopted in practice. 

51 THE HORIZON LINE The horizon at sea is that bounding circle 
of vision where the sea seems to meet the sky; on land, barring obstructions, it is 
that line where the sky and earth seem to meet and is at the heighth of the ob- 
servers eye, for to see farther, do we not mount up higher? It is evident that the 
plane of this horizon will be orthographically projected onto— really will intersect 

• —the picture plane, as a horizontal line through the vertical projection of the 
point of sight, hence we call such a line, the "horizon line" of the picture. 

52 THE APPLICATION OF THE DISTANCE POINTS. As has been 
stated, it is often inconvenient to use the horizontal projection of the point of 
sight, and to further faciliate the drawing, this point is disregarded and the dis- 
tance points for the drawing assumed. Perspective No. 1, Plate 23, is such a 
drawing, s' being the vertical projection of the point of sight, B-L the horizon 
line and d', d' the two distance points. This figure illustrates — beginning at the 
left — the perspective of a hollow cube, a hollow hexagonal prism, and a hollow 
cylinder. The method of procedure being that given in Sect. 49, as will be seen 
from the following:^ 



74 PERSPECTIVE. 

Let us consider the perspective of two points of each figure. 
THE CUBE. Consider the points 1 and 2, elevation, 1-2, plan; the perpendicular 
through 1 pierces V at 1, vanishes at s', and 1 — s' is its per- 
spective; the diagonal through the same point, pierces V at c, and van- 
ishes at d' (left;, and s shown in perspective as c-d', hence 1', the intersec- 
tion of these two perspectives, is the perspective of point 1. The diagonal through 
2 pierces V as c' (do not fail to note that the vertical projection of the diagonal 
must be drawn through the vertical projection of the point) and c'-d' is its per- 
spective; the perpendicular through point 2, pierces V at 2 and is shown 
in perspective as 2-s', which intersecting with c'-d' in 2', gives the required per- 
spective. Note that the lengths of the horizontal projection of the diagonals are 
equal — in this case they co-incide — and therefore the perspectives fall the same 
distance to the right of the elevation and the perspective l'-2', 
is parallel to the original line; from which we deduce, the perspective of a 
line which is parallel to the picture plane, is parallel to the line itself 

THE PRISM. Following the points indicated on-the drawing, as de- 

scribed from the cube, we note that either distance point may be used — according 
to the direction of the horizontal projection of the diagonal — and the same result 
obtained. 

THE CYLINDER. In this case we note it is more convenient to use the 
distance point on the right. Here we have the perspective of a curved line, which 
is found by taking a series of points and finding the perspective of each point, 
then joining these perspectives by a curve, or, the curve being a circle, it may be 
enclosed within a square and the perspective of the square found, and the required 
perspective inscribed within the perspective of the square. 

From the foregoing, we note that but one distance point is necessary, 
though two may be used to advantage. 
53 PRACTICAL PERSPECTIVE. Referring to the perspective just 

discussed, the confusion of the lines is at once remarked The Plate illustrates a 
very elementary example, and since we have confusion here, that resulting from a 
complex drawing, as the perspective of a house, may be surmised. In practice, the 
elevation is removed to one side and each point projected in, where, and as needed. 

Plate 23, depicting the perspective of a flight of steps, illustrates this prac- 
tical arrangement; P-Q-R-S shows the sheet of paper to receive the perspective — 
the picture plane^the plan is shown revolved into the first quadrant, and the eleva- 
tion, set to one side— in this case, the left side, though either right or left may be 
used. 

To find the perspective, we must have given a plan and one or more eleva- 
tions, according to the view desired, also the position assumed for the picture 
plane — one of parallelism or at an angle with the principal elevation ; these condi 
tions given, a view point is assumed (its vertical projection) and a distance point, 
or points, taken. 

Referring to Plate 23, we note. then, that the plan, elevation, s' and d', are 
given, and that the object is made up of two sets of parallel lines ; when this is the- 
case, that is. when an object has one or more sets of parallel lines, it expedites 
matters and renders the drawing more accurate, to find the vanishing point 
for each set of parallels. To do this, the horizontal projection of S is required, 
and is found by erecting a perpendicular through s' and laying off s-x (below) equal 
to s'-d'. or if this is not convenient, assume s to be revolved into the plane of the 



PERSPECTIVE. * 75 

picture, and draw s-x (above) equal to s'-d'. Now all of the lines of the steps 
are parallel to H and at either 60° or 30° with V and proceeding as in Sect. 46, we 
find the required vanishing points. CThe 30° vanishing point is without the drawing). 

Let us consider the finding- of one point in perspective, the point m (plan), 
where tlie front edge of the third step intersects the side wall, being chosen for 
example. The elevation of this point is up three steps; this heighth is then pro- 
jected in as the horizontal line o'-n'; the perpendicular through m, pierces V at 
n', s'-n' being its perspective; the diagonal through the point pierces V ato', o'- 
d' shows its perspective, and M, the intersection of these two perspectives, is the 
required perspective ; all other points are located in a similar manner. 

Referring to the plate, again, it will be noted that walks and a cut stone wall 
appear in the perspective drawing and do not appear in the given elevation ; these 
are "guessed ' in, — a practice in vogue, commecially, the procedure being, to 
accurately locate a number of principle points, then approximate the details 
and having vanishing points, known, the method is not at all a crude one, for after 
some little practice one is able to do very accurate work. 

NOTES 



76 



COLOR WORK 



TINTING 



54 INTRODUCTORY. Tinting is the art of applying colors to drawings 
and as a "touch of color" added to most things enhances their beauty, so does the 
art of tinting assist in the production ot handsome drawings. The art is much 
used in the preparation of drawings for catalogue illustrations, this particular 
kind of work being a trade'in itself and known as "wash drawing" The art of 
tinting, is, however, of some importance to the ordinary engineer-draughtsman, 
being much used by the architectual engineer for coloring- plans and perspectives 
of buildings and by others for expediting the drawing of sections, — the sectioned 
part being colored as a substitute for cross-hatching. 

55 OUTFIT. The outfit needed for the course as herein embodied, is as 
follows: 

(1). Two small beakers, for holding water. 

(2) Two sable or camel's hair brushes, or, if preferred, one double 
ended brush, — one end for color, the other for clear water. 
The brush should be shaped, thick in the body, tapering rapid- 
ly to a fine point. 

(3). A nest of six, cabinet saucers, in which to mix the colors. 

(4). A bottle of library paste, for mounting the paper. 

(5). A small hand sponge, or rag, with which to sponge the paper. 

(6). A six inch square of ordinary fly screening. 

(7). A tooth brush, or other small, stiff bristled brush. 

(8). One-half pan (trade term) of Chinese white. 

(9). A small stick of Chinese, or India black ink. 

The paper best adapted for tinting, differs from a good draAving paper in 
that it is comparatively rough of surface. 

56 MAKING A STRETCH. Since the tints are applied in a liquid form, 
there is more or less of a tendency for the paper to "blister", the moisture causing 
it to stretch and the corners being fixed, the paper blisters in proportion to the 
amount of the liquid applied. To meet this tendency, the paper is usu- 
ally "stretched" on the board. This is done as follows: — 

To make a stretch, first select the surface of the paper to receive the draw- 
ing, then lay the paper on a drawing board, drawing side up; now "square" the top 
edge of the paper with a T-square, then slide the square down for about |' ' and 
turn up this ^' ' strip of paper against the edge of the T-square blade, remove 
the square and fold the paper back; in this manner, turn up and fold back a strip of 
about X " at each side of the sheet, turning the top side first, then one end, then the 
other and lastly, the bottom side ; with the paper thus prepared, turn it over and 
with a sponge or rag, apply a liberal wash of clear water — being careful to keep it 



COLOR WORK— TINTING. 77 

off the up turned edges — and allow it to soak for two or three minutes, this ex 
pands the paper; should a very "tight" stretch be desired, the paper may be moist- 
ened on both sides ; for the exercises of this course, moistening on the under side 
will suffice) then turn it over on the drawing- board, squaring- the last turned edge 
with a line drawn on the board, and rub down, — the moist surface will adhere to 
the board for a short time; now apply a liberal coating of paste to the turned up 
strips, — being- careful to keep it off the surface to be drawn upon taking them in 
the reverse order as turned up, fold back and rub down until perfect cohesion is ob- 
tained ; when the paper is pasted on and while the paste is yet moist, the paper 
should be drawn taunt with the finger tips, this gives an additional stretch to the 
sheet, which, being yet moist, is now permitted to dry, thus contracting the 
expanded sheet and the pasted parts being fixed, the paper is stretched. 

57 MIXING THE COLORS. To mix the colors, dip one end of the 
brush into clear water and transfer a quantity of water to one of the cabinet sauc- 
ers—the quantity of water is proportional to the surface to be covered, a short 
experience enabling one to closely estimate — now apply the moist end to the color, 
rubbing slightly, then rub it in the saucer; repeat this operation until the desired 
tint has been obtained. 

58 FLAT WASH. A "flat wash", is the term applied to the application 
of a uniform tint, (See Plate 25). In applying the color, the brush should be well 
filled and a small "puddle" of color made on the surface to be colored ; the puddle 
is then washed over the surface, — we do not "paint" but "wash" — then picked up 
with a dry brush. This applies to fairly large surfaces, if the surface be small, the 
brush may contain little color and the surface be "painted". 

The tints, if permitted to stand on the paper, will dry in a very short time, 
especially along the outer edges, and when washed over and the sheet allowed to 
dry, these edges will give a streaked appearance ; for this reason it is important to 
keep all parts of the wash moving— the minimum speed is quickly ascertained in 
practice— until the wash is finished.. If one cannot work with sufficient rapidity, 
the drying tendency may be minimized by first moistening the surface with clear 
water. Such a procedure is, also, advantageous as a vehicle for carrying the wash 
into intricate parts of the drawing, since the water can be applied slowly and with 
necessary caution to preserve lines, however, when so doing, care must be exer- 
cised to produce a uniform tint, as the added water will lighten it. 

59 SHADING. There are a number of methods for shading with tints, 
principle among which are the following: — 

1. To shade by means of flat tints, lay on a light tint flat wash for a short 
space, then soften off the edge with a clear, moist brush-end; when dry, begin as 
before, and this time carry the wash a little greater distance, then soften off the 
edge as above; in this manner, apply a number of coatings, each successive one 
covering all the others. — a process which causes the first applied wash to become 
darkest and grades from it to the last wash. The objection to this method is the 
great amount of time consumed in its application. 

2. A second method of applying shades, is to mix tlie color to correspond to 
the deepest shade, then apply a liberal amount to the surface; then pick up a 
quantity of clear water with the brush and add this to the color on the sheet, 
washing down for a short distance, then add more water and wash down, etc. 
adding clear water each time, thus thinning the tint and grading the wash from' 

L.ofC. 



78 COLOR WORK- TINTING. 

dark to lig-ht. This method requires much practice to determine.the exact amount 
of water for a uniform grading" of the tint. 

3. A third method, is to begin as in the second method, thin the color off the 
sheet — in the saucers — then apply. In these two methods it is important that a 
fair sized puddle be maintained on the paper, thus insuring a more even thin- 
ning of the color and a uniform grading of the tint. Too much water will produce 
a streak, too little, no perceptible change of tint. 

4. When the surface is comparatively small, a fourth method may be used to 
advantage. Here, apply a small amount of the heavy tint, then with a clean, moist 
brush draw the color out, and as it is carried over the surface it becomes thinned 
and the color g-raded from the original dark to light. The exact amount to first 
apply is a matter of practice. 

To miminize a tendency to dry too rapidly, clear water may be first ap- 
plied, though for shading, the surface must be allowed to dry to a point where the 
"glisten" of the water disappears from the surface of the paper, else the color will 
follow the water and cannot be controlled. 

NOTES 



79 



STIPPLING 

60 INTRODUCTORY. To "stipple", means to shade by means of dots. If 
the surface to be stippled is small, the work is usually done with a pen point; if 
the surface is of some size, such a method is too time consuming and difficult 
where g'ood results are desired. For stippling' such surfaces, there are several 
mechanical methods which may be used : that method to be followed in this course, 
will be treated of as being typical of these processes. 

If a piece of ordinary wire fly screening be held over a sheet ef paper and a 
stiff brush — such as a tooth brush — containing a liquid, be brushed over the upper 
surface, it will throw dots of the liquid onto the paper. This simple procedure 
is the method to be followed in executing the exercises in stippling. 

61 METHOD OF PROCEDURE. For good results the paper is stretched 
as for tinting, though if the amount of surface to be stippled is small, and the 
degree of shade comparatively light, the paper may be secured with thumb tacks 
as in ordinary drawing. The color is mixed as for tinting, however, no very light 
tints are used as the light shade is here produced in a different manner. The fig- 
ure to be "drawn", is executed on a sheet of fairly stiff paper — not the finished 
sheet — and is then prepared for strippling by cutting out one surface at a time, 
that is, we make a template for the surface, lay this on the paper, matting out all 
other parts, then throw the dots on the exposed area. 

To stipple, dip the brush in the color, shake it until quite dry, then brush 
across the screen. If the brush contains too much color the dots will not be clean 
cut and often will run tog-ether and blur and blot. 

To shade lightly and uniformly, hold the screen some distance away — three 
or four inches — from the paper; as the screen is moved closer the shading may yet 
be uniform, but will grow darker. Large surfaces are stippled by moving the 
screen about and shades intensified, by holding the screen in one place and close to 
the paper. 



Press of 

MURPHEY-BIVINS COMPANY, 

LaFavette, Ind. 



JAN 5'^ "trc 



